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Multiple choice
In the Deutsch-Jozsa algorithm cast as an HSP over
G
=
Z
2
n
G = \mathbb{Z}_2^n
G
=
Z
2
n
, the final
H
⊗
n
H^{\otimes n}
H
⊗
n
gives the all-zeros outcome amplitude
α
=
(
1
/
2
n
)
∑
x
(
−
1
)
f
(
x
)
\alpha = (1/2^n) \sum_x (-1)^{f(x)}
α
=
(
1/
2
n
)
∑
x
(
−
1
)
f
(
x
)
. What does measuring
0
n
0^n
0
n
tell you?
It occurs with probability
1
/
2
1/2
1/2
in both the constant and balanced cases
It never occurs in either case, so the measurement carries no information
It occurs with certainty when f is constant and never when f is balanced, so
0
n
0^n
0
n
distinguishes the two cases in a single shot
It occurs with certainty when f is balanced and never when f is constant
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